Chaos, complexity and morphogenesis: optical-pattern formation and recognition

Year: 1994

Authors: Arecchi F.T.

Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy; Department of Physics, University of Firenze, 50125 Firenze, Italy

Abstract: In 1952 A Turing introduced the concept of chemical morphogenesis. A medium with at least two interacting and diffusing components (activator and inhibitor) can be subjected to spontaneous pattern formation, with a scale length independent of the boundary conditions, and thus maintained even in the infinite volume limit. This is at variance with pattern formation in fluids (as, e.g., Rayleigh-Benard and Faraday instabilities) where the size is imposed by the boundary geometry. In non-linear optics, patterns emerge from the coupling of a diffractive equation describing electromagnetic propagation with a diffusion equation describing the local modification of the polarizability in a medium. As we adjust an extensive parameter (the so-called Fresnel number F) corresponding to the optical aspect ratio, we observe a transition from a regime dominated by the boundary constraints to a Turing-type regime dominated by the bulk parameter. This is equivalent to saying that the preminent role is due to the diffractive equation in one case and to the diffusive one in the other. Morphogenesis for low F arises from the non-linear competition among a small number of degrees of freedom, giving rise to a space-uniform excitation with a low-dimensional dynamics. This gives rise to the different scenarios of chaos. Their properties have been explored in the past decade. In the large-F case, the space-time instabilities rapidly evolve toward complex patterns, not reducible to a few indicators. In the case of two-dimensional fields, global characterization is achieved via the statistics of the topological defects.

Journal/Review: NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA D-CONDENSED MATTER ATOMIC MOLECULAR AND CHEMICAL PHYSICS FLUIDS PLASMAS BIOPHYSICS

Volume: 16 (8)      Pages from: 1065  to: 1089

KeyWords: FEEDBACK MIRROR
DOI: 10.1007/BF02458788

Citations: 4
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